The present embodiments relate to computing soft tissue deformations, such as for medical imaging, computer animation, or gaming. Determining organ deformation may be important for medical image reconstruction, medical image registration, digital twin modeling for data integration and outcome prediction, three-dimensional (3D) mesh editing, augmented or virtual reality, or other applications.
Biomechanical models of soft tissue (e.g., as priors or constraints) may provide more realistic capabilities for determining their deformation under various conditions (e.g. subject to external forces like pressure or gravity, internal forces like stiffness or active stress, etc.). Current state of the art explicitly solves biomechanical equations using the finite element method or other integration methods, given boundary conditions, external forces, constitutive laws and model parameters. Although accurate, these methods are unfortunately time consuming, requiring minutes to hours of computation for a high-fidelity simulation. Real-time solutions exist (e.g., mass-spring or mesh-free models), however at a price for accuracy.
Methods based on machine learning or statistical learning for biophysical simulations have been explored, mostly for computational fluid dynamics (CFD). A common approach (e.g., Proper Orthogonal Decomposition (POD)) estimates a subspace of solutions from a database of simulations. The solutions of the CFD equations are solved in the subspace, and the final solution is reconstructed accordingly. This approach assumes that the solution can be reconstructed by a linear combination of basis functions, which may not be the case. As a result, the accuracy of the reconstructed result could be sub-optimal. Similar approaches have been investigated for soft-tissue mechanics as well and other physical systems.
More sophisticated data-driven techniques have been proposed, such as a random-forest approach to solve in real-time CFD for fluid simulations, based on particle-based solvers. An acceleration at large time step is predicted given the intrinsic properties of a fluid particle and its direct neighborhood. The prediction is a regression model, represented using random forests and trained on thousands of simulations. This approach showed fast simulation performance. However, it is especially tailored to the CFD problem and would not apply directly to biomechanics or other modeling of soft tissue: the states are different, soft tissue are solid material with varying stiffness, and solver stability is much more crucial and difficult to maintain in biomechanics due to the increase stiffness of the partial differential equations. In particular, the random forest approach suffers from high frequency numerical errors that would make the computation not tractable.
Model reduction for fast computation of deformable material has been used with good results in computer graphics, in fluid simulation, in the video game industry and computer assisted design. While these methods perform model reduction on the space of deformations of the object, newer approaches perform reduction on the material model of the object. The range of uses of these methods has not tackled more physiologically accurate, and hence more realistic biomechanical models.